Python: How to parent an object to a bone without transformation?
You can do this using bpy.ops.object.parent_set() and using the keep_transform parameter. I also allowed to choose which bone of your armature you want it to be the parent by setting parent_bone = 'BoneNameYouWantToBeParent'as shown below:

import bpy

ob= bpy.data.objects['Cube']
arma = bpy.data.objects['Armature']

bpy.ops.object.select_all(action='DESELECT')
arma.select = True
bpy.context.scene.objects.active = arma 

bpy.ops.object.mode_set(mode='EDIT')

parent_bone = 'Bone' # choose the bone name which you want to be the parent

arma.data.edit_bones.active = arma.data.edit_bones[parent_bone]

bpy.ops.object.mode_set(mode='OBJECT')

bpy.ops.object.select_all(action='DESELECT') #deselect all objects
ob.select = True
arma.select = True
bpy.context.scene.objects.active = arma    #the active object will be the parent of all selected object

bpy.ops.object.parent_set(type='BONE', keep_transform=True)


As shown below I modified your armature to have multiple bones so you can select which bone you want it to be the parent to your Cube. In the below screenshot I used Bone to be the parent:



In the screenshot below I chose Bone.001 to be the parent:



Updated .blend file can be found here: